// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 David Harmon <dharmon@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H
#define EIGEN_ARPACKGENERALIZEDSELFADJOINTEIGENSOLVER_H

#include "../../../../Eigen/Dense"

namespace Eigen {

namespace internal {
    template <typename Scalar, typename RealScalar> struct arpack_wrapper;
    template <typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP;
}  // namespace internal

template <typename MatrixType, typename MatrixSolver = SimplicialLLT<MatrixType>, bool BisSPD = false> class ArpackGeneralizedSelfAdjointEigenSolver
{
public:
    //typedef typename MatrixSolver::MatrixType MatrixType;

    /** \brief Scalar type for matrices of type \p MatrixType. */
    typedef typename MatrixType::Scalar Scalar;
    typedef typename MatrixType::Index Index;

    /** \brief Real scalar type for \p MatrixType.
   *
   * This is just \c Scalar if #Scalar is real (e.g., \c float or
   * \c Scalar), and the type of the real part of \c Scalar if #Scalar is
   * complex.
   */
    typedef typename NumTraits<Scalar>::Real RealScalar;

    /** \brief Type for vector of eigenvalues as returned by eigenvalues().
   *
   * This is a column vector with entries of type #RealScalar.
   * The length of the vector is the size of \p nbrEigenvalues.
   */
    typedef typename internal::plain_col_type<MatrixType, RealScalar>::type RealVectorType;

    /** \brief Default constructor.
   *
   * The default constructor is for cases in which the user intends to
   * perform decompositions via compute().
   *
   */
    ArpackGeneralizedSelfAdjointEigenSolver() : m_eivec(), m_eivalues(), m_isInitialized(false), m_eigenvectorsOk(false), m_nbrConverged(0), m_nbrIterations(0)
    {
    }

    /** \brief Constructor; computes generalized eigenvalues of given matrix with respect to another matrix.
   *
   * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
   *    computed. By default, the upper triangular part is used, but can be changed
   *    through the template parameter.
   * \param[in] B Self-adjoint matrix for the generalized eigenvalue problem.
   * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
   *    Must be less than the size of the input matrix, or an error is returned.
   * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
   *    respective meanings to find the largest magnitude , smallest magnitude,
   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
   *    value can contain floating point value in string form, in which case the
   *    eigenvalues closest to this value will be found.
   * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
   * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
   *    means machine precision.
   *
   * This constructor calls compute(const MatrixType&, const MatrixType&, Index, string, int, RealScalar)
   * to compute the eigenvalues of the matrix \p A with respect to \p B. The eigenvectors are computed if
   * \p options equals #ComputeEigenvectors.
   *
   */
    ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
                                            const MatrixType& B,
                                            Index nbrEigenvalues,
                                            std::string eigs_sigma = "LM",
                                            int options = ComputeEigenvectors,
                                            RealScalar tol = 0.0)
        : m_eivec(), m_eivalues(), m_isInitialized(false), m_eigenvectorsOk(false), m_nbrConverged(0), m_nbrIterations(0)
    {
        compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);
    }

    /** \brief Constructor; computes eigenvalues of given matrix.
   *
   * \param[in] A Self-adjoint matrix whose eigenvalues / eigenvectors will
   *    computed. By default, the upper triangular part is used, but can be changed
   *    through the template parameter.
   * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
   *    Must be less than the size of the input matrix, or an error is returned.
   * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
   *    respective meanings to find the largest magnitude , smallest magnitude,
   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
   *    value can contain floating point value in string form, in which case the
   *    eigenvalues closest to this value will be found.
   * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
   * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
   *    means machine precision.
   *
   * This constructor calls compute(const MatrixType&, Index, string, int, RealScalar)
   * to compute the eigenvalues of the matrix \p A. The eigenvectors are computed if
   * \p options equals #ComputeEigenvectors.
   *
   */

    ArpackGeneralizedSelfAdjointEigenSolver(const MatrixType& A,
                                            Index nbrEigenvalues,
                                            std::string eigs_sigma = "LM",
                                            int options = ComputeEigenvectors,
                                            RealScalar tol = 0.0)
        : m_eivec(), m_eivalues(), m_isInitialized(false), m_eigenvectorsOk(false), m_nbrConverged(0), m_nbrIterations(0)
    {
        compute(A, nbrEigenvalues, eigs_sigma, options, tol);
    }

    /** \brief Computes generalized eigenvalues / eigenvectors of given matrix using the external ARPACK library.
   *
   * \param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.
   * \param[in]  B  Selfadjoint matrix for generalized eigenvalues.
   * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
   *    Must be less than the size of the input matrix, or an error is returned.
   * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
   *    respective meanings to find the largest magnitude , smallest magnitude,
   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
   *    value can contain floating point value in string form, in which case the
   *    eigenvalues closest to this value will be found.
   * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
   * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
   *    means machine precision.
   *
   * \returns    Reference to \c *this
   *
   * This function computes the generalized eigenvalues of \p A with respect to \p B using ARPACK.  The eigenvalues()
   * function can be used to retrieve them.  If \p options equals #ComputeEigenvectors,
   * then the eigenvectors are also computed and can be retrieved by
   * calling eigenvectors().
   *
   */
    ArpackGeneralizedSelfAdjointEigenSolver& compute(const MatrixType& A,
                                                     const MatrixType& B,
                                                     Index nbrEigenvalues,
                                                     std::string eigs_sigma = "LM",
                                                     int options = ComputeEigenvectors,
                                                     RealScalar tol = 0.0);

    /** \brief Computes eigenvalues / eigenvectors of given matrix using the external ARPACK library.
   *
   * \param[in]  A  Selfadjoint matrix whose eigendecomposition is to be computed.
   * \param[in] nbrEigenvalues The number of eigenvalues / eigenvectors to compute.
   *    Must be less than the size of the input matrix, or an error is returned.
   * \param[in] eigs_sigma String containing either "LM", "SM", "LA", or "SA", with
   *    respective meanings to find the largest magnitude , smallest magnitude,
   *    largest algebraic, or smallest algebraic eigenvalues. Alternatively, this
   *    value can contain floating point value in string form, in which case the
   *    eigenvalues closest to this value will be found.
   * \param[in]  options Can be #ComputeEigenvectors (default) or #EigenvaluesOnly.
   * \param[in] tol What tolerance to find the eigenvalues to. Default is 0, which
   *    means machine precision.
   *
   * \returns    Reference to \c *this
   *
   * This function computes the eigenvalues of \p A using ARPACK.  The eigenvalues()
   * function can be used to retrieve them.  If \p options equals #ComputeEigenvectors,
   * then the eigenvectors are also computed and can be retrieved by
   * calling eigenvectors().
   *
   */
    ArpackGeneralizedSelfAdjointEigenSolver&
    compute(const MatrixType& A, Index nbrEigenvalues, std::string eigs_sigma = "LM", int options = ComputeEigenvectors, RealScalar tol = 0.0);

    /** \brief Returns the eigenvectors of given matrix.
   *
   * \returns  A const reference to the matrix whose columns are the eigenvectors.
   *
   * \pre The eigenvectors have been computed before.
   *
   * Column \f$ k \f$ of the returned matrix is an eigenvector corresponding
   * to eigenvalue number \f$ k \f$ as returned by eigenvalues().  The
   * eigenvectors are normalized to have (Euclidean) norm equal to one. If
   * this object was used to solve the eigenproblem for the selfadjoint
   * matrix \f$ A \f$, then the matrix returned by this function is the
   * matrix \f$ V \f$ in the eigendecomposition \f$ A V = D V \f$.
   * For the generalized eigenproblem, the matrix returned is the solution \f$ A V = D B V \f$
   *
   * Example: \include SelfAdjointEigenSolver_eigenvectors.cpp
   * Output: \verbinclude SelfAdjointEigenSolver_eigenvectors.out
   *
   * \sa eigenvalues()
   */
    const Matrix<Scalar, Dynamic, Dynamic>& eigenvectors() const
    {
        eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
        eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
        return m_eivec;
    }

    /** \brief Returns the eigenvalues of given matrix.
   *
   * \returns A const reference to the column vector containing the eigenvalues.
   *
   * \pre The eigenvalues have been computed before.
   *
   * The eigenvalues are repeated according to their algebraic multiplicity,
   * so there are as many eigenvalues as rows in the matrix. The eigenvalues
   * are sorted in increasing order.
   *
   * Example: \include SelfAdjointEigenSolver_eigenvalues.cpp
   * Output: \verbinclude SelfAdjointEigenSolver_eigenvalues.out
   *
   * \sa eigenvectors(), MatrixBase::eigenvalues()
   */
    const Matrix<Scalar, Dynamic, 1>& eigenvalues() const
    {
        eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
        return m_eivalues;
    }

    /** \brief Computes the positive-definite square root of the matrix.
   *
   * \returns the positive-definite square root of the matrix
   *
   * \pre The eigenvalues and eigenvectors of a positive-definite matrix
   * have been computed before.
   *
   * The square root of a positive-definite matrix \f$ A \f$ is the
   * positive-definite matrix whose square equals \f$ A \f$. This function
   * uses the eigendecomposition \f$ A = V D V^{-1} \f$ to compute the
   * square root as \f$ A^{1/2} = V D^{1/2} V^{-1} \f$.
   *
   * Example: \include SelfAdjointEigenSolver_operatorSqrt.cpp
   * Output: \verbinclude SelfAdjointEigenSolver_operatorSqrt.out
   *
   * \sa operatorInverseSqrt(),
   *     \ref MatrixFunctions_Module "MatrixFunctions Module"
   */
    Matrix<Scalar, Dynamic, Dynamic> operatorSqrt() const
    {
        eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
        eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
        return m_eivec * m_eivalues.cwiseSqrt().asDiagonal() * m_eivec.adjoint();
    }

    /** \brief Computes the inverse square root of the matrix.
   *
   * \returns the inverse positive-definite square root of the matrix
   *
   * \pre The eigenvalues and eigenvectors of a positive-definite matrix
   * have been computed before.
   *
   * This function uses the eigendecomposition \f$ A = V D V^{-1} \f$ to
   * compute the inverse square root as \f$ V D^{-1/2} V^{-1} \f$. This is
   * cheaper than first computing the square root with operatorSqrt() and
   * then its inverse with MatrixBase::inverse().
   *
   * Example: \include SelfAdjointEigenSolver_operatorInverseSqrt.cpp
   * Output: \verbinclude SelfAdjointEigenSolver_operatorInverseSqrt.out
   *
   * \sa operatorSqrt(), MatrixBase::inverse(),
   *     \ref MatrixFunctions_Module "MatrixFunctions Module"
   */
    Matrix<Scalar, Dynamic, Dynamic> operatorInverseSqrt() const
    {
        eigen_assert(m_isInitialized && "SelfAdjointEigenSolver is not initialized.");
        eigen_assert(m_eigenvectorsOk && "The eigenvectors have not been computed together with the eigenvalues.");
        return m_eivec * m_eivalues.cwiseInverse().cwiseSqrt().asDiagonal() * m_eivec.adjoint();
    }

    /** \brief Reports whether previous computation was successful.
   *
   * \returns \c Success if computation was successful, \c NoConvergence otherwise.
   */
    ComputationInfo info() const
    {
        eigen_assert(m_isInitialized && "ArpackGeneralizedSelfAdjointEigenSolver is not initialized.");
        return m_info;
    }

    size_t getNbrConvergedEigenValues() const { return m_nbrConverged; }

    size_t getNbrIterations() const { return m_nbrIterations; }

protected:
    Matrix<Scalar, Dynamic, Dynamic> m_eivec;
    Matrix<Scalar, Dynamic, 1> m_eivalues;
    ComputationInfo m_info;
    bool m_isInitialized;
    bool m_eigenvectorsOk;

    size_t m_nbrConverged;
    size_t m_nbrIterations;
};

template <typename MatrixType, typename MatrixSolver, bool BisSPD>
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>::compute(const MatrixType& A,
                                                                                   Index nbrEigenvalues,
                                                                                   std::string eigs_sigma,
                                                                                   int options,
                                                                                   RealScalar tol)
{
    MatrixType B(0, 0);
    compute(A, B, nbrEigenvalues, eigs_sigma, options, tol);

    return *this;
}

template <typename MatrixType, typename MatrixSolver, bool BisSPD>
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>&
ArpackGeneralizedSelfAdjointEigenSolver<MatrixType, MatrixSolver, BisSPD>::compute(const MatrixType& A,
                                                                                   const MatrixType& B,
                                                                                   Index nbrEigenvalues,
                                                                                   std::string eigs_sigma,
                                                                                   int options,
                                                                                   RealScalar tol)
{
    eigen_assert(A.cols() == A.rows());
    eigen_assert(B.cols() == B.rows());
    eigen_assert(B.rows() == 0 || A.cols() == B.rows());
    eigen_assert((options & ~(EigVecMask | GenEigMask)) == 0 && (options & EigVecMask) != EigVecMask && "invalid option parameter");

    bool isBempty = (B.rows() == 0) || (B.cols() == 0);

    // For clarity, all parameters match their ARPACK name
    //
    // Always 0 on the first call
    //
    int ido = 0;

    int n = (int)A.cols();

    // User options: "LA", "SA", "SM", "LM", "BE"
    //
    char whch[3] = "LM";

    // Specifies the shift if iparam[6] = { 3, 4, 5 }, not used if iparam[6] = { 1, 2 }
    //
    RealScalar sigma = 0.0;

    if (eigs_sigma.length() >= 2 && isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1]))
    {
        eigs_sigma[0] = toupper(eigs_sigma[0]);
        eigs_sigma[1] = toupper(eigs_sigma[1]);

        // In the following special case we're going to invert the problem, since solving
        // for larger magnitude is much much faster
        // i.e., if 'SM' is specified, we're going to really use 'LM', the default
        //
        if (eigs_sigma.substr(0, 2) != "SM")
        {
            whch[0] = eigs_sigma[0];
            whch[1] = eigs_sigma[1];
        }
    }
    else
    {
        eigen_assert(false && "Specifying clustered eigenvalues is not yet supported!");

        // If it's not scalar values, then the user may be explicitly
        // specifying the sigma value to cluster the evs around
        //
        sigma = atof(eigs_sigma.c_str());

        // If atof fails, it returns 0.0, which is a fine default
        //
    }

    // "I" means normal eigenvalue problem, "G" means generalized
    //
    char bmat[2] = "I";
    if (eigs_sigma.substr(0, 2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])) || (!isBempty && !BisSPD))
        bmat[0] = 'G';

    // Now we determine the mode to use
    //
    int mode = (bmat[0] == 'G') + 1;
    if (eigs_sigma.substr(0, 2) == "SM" || !(isalpha(eigs_sigma[0]) && isalpha(eigs_sigma[1])))
    {
        // We're going to use shift-and-invert mode, and basically find
        // the largest eigenvalues of the inverse operator
        //
        mode = 3;
    }

    // The user-specified number of eigenvalues/vectors to compute
    //
    int nev = (int)nbrEigenvalues;

    // Allocate space for ARPACK to store the residual
    //
    Scalar* resid = new Scalar[n];

    // Number of Lanczos vectors, must satisfy nev < ncv <= n
    // Note that this indicates that nev != n, and we cannot compute
    // all eigenvalues of a mtrix
    //
    int ncv = std::min(std::max(2 * nev, 20), n);

    // The working n x ncv matrix, also store the final eigenvectors (if computed)
    //
    Scalar* v = new Scalar[n * ncv];
    int ldv = n;

    // Working space
    //
    Scalar* workd = new Scalar[3 * n];
    int lworkl = ncv * ncv + 8 * ncv;  // Must be at least this length
    Scalar* workl = new Scalar[lworkl];

    int* iparam = new int[11];
    iparam[0] = 1;  // 1 means we let ARPACK perform the shifts, 0 means we'd have to do it
    iparam[2] = std::max(300, (int)std::ceil(2 * n / std::max(ncv, 1)));
    iparam[6] = mode;  // The mode, 1 is standard ev problem, 2 for generalized ev, 3 for shift-and-invert

    // Used during reverse communicate to notify where arrays start
    //
    int* ipntr = new int[11];

    // Error codes are returned in here, initial value of 0 indicates a random initial
    // residual vector is used, any other values means resid contains the initial residual
    // vector, possibly from a previous run
    //
    int info = 0;

    Scalar scale = 1.0;
    //if (!isBempty)
    //{
    //Scalar scale = B.norm() / std::sqrt(n);
    //scale = std::pow(2, std::floor(std::log(scale+1)));
    ////M /= scale;
    //for (size_t i=0; i<(size_t)B.outerSize(); i++)
    //    for (typename MatrixType::InnerIterator it(B, i); it; ++it)
    //        it.valueRef() /= scale;
    //}

    MatrixSolver OP;
    if (mode == 1 || mode == 2)
    {
        if (!isBempty)
            OP.compute(B);
    }
    else if (mode == 3)
    {
        if (sigma == 0.0)
        {
            OP.compute(A);
        }
        else
        {
            // Note: We will never enter here because sigma must be 0.0
            //
            if (isBempty)
            {
                MatrixType AminusSigmaB(A);
                for (Index i = 0; i < A.rows(); ++i) AminusSigmaB.coeffRef(i, i) -= sigma;

                OP.compute(AminusSigmaB);
            }
            else
            {
                MatrixType AminusSigmaB = A - sigma * B;
                OP.compute(AminusSigmaB);
            }
        }
    }

    if (!(mode == 1 && isBempty) && !(mode == 2 && isBempty) && OP.info() != Success)
        std::cout << "Error factoring matrix" << std::endl;

    do
    {
        internal::arpack_wrapper<Scalar, RealScalar>::saupd(
            &ido, bmat, &n, whch, &nev, &tol, resid, &ncv, v, &ldv, iparam, ipntr, workd, workl, &lworkl, &info);

        if (ido == -1 || ido == 1)
        {
            Scalar* in = workd + ipntr[0] - 1;
            Scalar* out = workd + ipntr[1] - 1;

            if (ido == 1 && mode != 2)
            {
                Scalar* out2 = workd + ipntr[2] - 1;
                if (isBempty || mode == 1)
                    Matrix<Scalar, Dynamic, 1>::Map(out2, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
                else
                    Matrix<Scalar, Dynamic, 1>::Map(out2, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);

                in = workd + ipntr[2] - 1;
            }

            if (mode == 1)
            {
                if (isBempty)
                {
                    // OP = A
                    //
                    Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);
                }
                else
                {
                    // OP = L^{-1}AL^{-T}
                    //
                    internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::applyOP(OP, A, n, in, out);
                }
            }
            else if (mode == 2)
            {
                if (ido == 1)
                    Matrix<Scalar, Dynamic, 1>::Map(in, n) = A * Matrix<Scalar, Dynamic, 1>::Map(in, n);

                // OP = B^{-1} A
                //
                Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
            }
            else if (mode == 3)
            {
                // OP = (A-\sigmaB)B (\sigma could be 0, and B could be I)
                // The B * in is already computed and stored at in if ido == 1
                //
                if (ido == 1 || isBempty)
                    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
                else
                    Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.solve(B * Matrix<Scalar, Dynamic, 1>::Map(in, n));
            }
        }
        else if (ido == 2)
        {
            Scalar* in = workd + ipntr[0] - 1;
            Scalar* out = workd + ipntr[1] - 1;

            if (isBempty || mode == 1)
                Matrix<Scalar, Dynamic, 1>::Map(out, n) = Matrix<Scalar, Dynamic, 1>::Map(in, n);
            else
                Matrix<Scalar, Dynamic, 1>::Map(out, n) = B * Matrix<Scalar, Dynamic, 1>::Map(in, n);
        }
    } while (ido != 99);

    if (info == 1)
        m_info = NoConvergence;
    else if (info == 3)
        m_info = NumericalIssue;
    else if (info < 0)
        m_info = InvalidInput;
    else if (info != 0)
        eigen_assert(false && "Unknown ARPACK return value!");
    else
    {
        // Do we compute eigenvectors or not?
        //
        int rvec = (options & ComputeEigenvectors) == ComputeEigenvectors;

        // "A" means "All", use "S" to choose specific eigenvalues (not yet supported in ARPACK))
        //
        char howmny[2] = "A";

        // if howmny == "S", specifies the eigenvalues to compute (not implemented in ARPACK)
        //
        int* select = new int[ncv];

        // Final eigenvalues
        //
        m_eivalues.resize(nev, 1);

        internal::arpack_wrapper<Scalar, RealScalar>::seupd(&rvec,
                                                            howmny,
                                                            select,
                                                            m_eivalues.data(),
                                                            v,
                                                            &ldv,
                                                            &sigma,
                                                            bmat,
                                                            &n,
                                                            whch,
                                                            &nev,
                                                            &tol,
                                                            resid,
                                                            &ncv,
                                                            v,
                                                            &ldv,
                                                            iparam,
                                                            ipntr,
                                                            workd,
                                                            workl,
                                                            &lworkl,
                                                            &info);

        if (info == -14)
            m_info = NoConvergence;
        else if (info != 0)
            m_info = InvalidInput;
        else
        {
            if (rvec)
            {
                m_eivec.resize(A.rows(), nev);
                for (int i = 0; i < nev; i++)
                    for (int j = 0; j < n; j++) m_eivec(j, i) = v[i * n + j] / scale;

                if (mode == 1 && !isBempty && BisSPD)
                    internal::OP<MatrixSolver, MatrixType, Scalar, BisSPD>::project(OP, n, nev, m_eivec.data());

                m_eigenvectorsOk = true;
            }

            m_nbrIterations = iparam[2];
            m_nbrConverged = iparam[4];

            m_info = Success;
        }

        delete[] select;
    }

    delete[] v;
    delete[] iparam;
    delete[] ipntr;
    delete[] workd;
    delete[] workl;
    delete[] resid;

    m_isInitialized = true;

    return *this;
}

// Single precision
//
extern "C" void ssaupd_(int* ido,
                        char* bmat,
                        int* n,
                        char* which,
                        int* nev,
                        float* tol,
                        float* resid,
                        int* ncv,
                        float* v,
                        int* ldv,
                        int* iparam,
                        int* ipntr,
                        float* workd,
                        float* workl,
                        int* lworkl,
                        int* info);

extern "C" void sseupd_(int* rvec,
                        char* All,
                        int* select,
                        float* d,
                        float* z,
                        int* ldz,
                        float* sigma,
                        char* bmat,
                        int* n,
                        char* which,
                        int* nev,
                        float* tol,
                        float* resid,
                        int* ncv,
                        float* v,
                        int* ldv,
                        int* iparam,
                        int* ipntr,
                        float* workd,
                        float* workl,
                        int* lworkl,
                        int* ierr);

// Double precision
//
extern "C" void dsaupd_(int* ido,
                        char* bmat,
                        int* n,
                        char* which,
                        int* nev,
                        double* tol,
                        double* resid,
                        int* ncv,
                        double* v,
                        int* ldv,
                        int* iparam,
                        int* ipntr,
                        double* workd,
                        double* workl,
                        int* lworkl,
                        int* info);

extern "C" void dseupd_(int* rvec,
                        char* All,
                        int* select,
                        double* d,
                        double* z,
                        int* ldz,
                        double* sigma,
                        char* bmat,
                        int* n,
                        char* which,
                        int* nev,
                        double* tol,
                        double* resid,
                        int* ncv,
                        double* v,
                        int* ldv,
                        int* iparam,
                        int* ipntr,
                        double* workd,
                        double* workl,
                        int* lworkl,
                        int* ierr);

namespace internal {

    template <typename Scalar, typename RealScalar> struct arpack_wrapper
    {
        static inline void saupd(int* ido,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 RealScalar* tol,
                                 Scalar* resid,
                                 int* ncv,
                                 Scalar* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 Scalar* workd,
                                 Scalar* workl,
                                 int* lworkl,
                                 int* info)
        {
            EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
        }

        static inline void seupd(int* rvec,
                                 char* All,
                                 int* select,
                                 Scalar* d,
                                 Scalar* z,
                                 int* ldz,
                                 RealScalar* sigma,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 RealScalar* tol,
                                 Scalar* resid,
                                 int* ncv,
                                 Scalar* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 Scalar* workd,
                                 Scalar* workl,
                                 int* lworkl,
                                 int* ierr)
        {
            EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
        }
    };

    template <> struct arpack_wrapper<float, float>
    {
        static inline void saupd(int* ido,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 float* tol,
                                 float* resid,
                                 int* ncv,
                                 float* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 float* workd,
                                 float* workl,
                                 int* lworkl,
                                 int* info)
        {
            ssaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
        }

        static inline void seupd(int* rvec,
                                 char* All,
                                 int* select,
                                 float* d,
                                 float* z,
                                 int* ldz,
                                 float* sigma,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 float* tol,
                                 float* resid,
                                 int* ncv,
                                 float* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 float* workd,
                                 float* workl,
                                 int* lworkl,
                                 int* ierr)
        {
            sseupd_(rvec, All, select, d, z, ldz, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, ierr);
        }
    };

    template <> struct arpack_wrapper<double, double>
    {
        static inline void saupd(int* ido,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 double* tol,
                                 double* resid,
                                 int* ncv,
                                 double* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 double* workd,
                                 double* workl,
                                 int* lworkl,
                                 int* info)
        {
            dsaupd_(ido, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, info);
        }

        static inline void seupd(int* rvec,
                                 char* All,
                                 int* select,
                                 double* d,
                                 double* z,
                                 int* ldz,
                                 double* sigma,
                                 char* bmat,
                                 int* n,
                                 char* which,
                                 int* nev,
                                 double* tol,
                                 double* resid,
                                 int* ncv,
                                 double* v,
                                 int* ldv,
                                 int* iparam,
                                 int* ipntr,
                                 double* workd,
                                 double* workl,
                                 int* lworkl,
                                 int* ierr)
        {
            dseupd_(rvec, All, select, d, v, ldv, sigma, bmat, n, which, nev, tol, resid, ncv, v, ldv, iparam, ipntr, workd, workl, lworkl, ierr);
        }
    };

    template <typename MatrixSolver, typename MatrixType, typename Scalar, bool BisSPD> struct OP
    {
        static inline void applyOP(MatrixSolver& OP, const MatrixType& A, int n, Scalar* in, Scalar* out);
        static inline void project(MatrixSolver& OP, int n, int k, Scalar* vecs);
    };

    template <typename MatrixSolver, typename MatrixType, typename Scalar> struct OP<MatrixSolver, MatrixType, Scalar, true>
    {
        static inline void applyOP(MatrixSolver& OP, const MatrixType& A, int n, Scalar* in, Scalar* out)
        {
            // OP = L^{-1} A L^{-T}  (B = LL^T)
            //
            // First solve L^T out = in
            //
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixU().solve(Matrix<Scalar, Dynamic, 1>::Map(in, n));
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationPinv() * Matrix<Scalar, Dynamic, 1>::Map(out, n);

            // Then compute out = A out
            //
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = A * Matrix<Scalar, Dynamic, 1>::Map(out, n);

            // Then solve L out = out
            //
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.permutationP() * Matrix<Scalar, Dynamic, 1>::Map(out, n);
            Matrix<Scalar, Dynamic, 1>::Map(out, n) = OP.matrixL().solve(Matrix<Scalar, Dynamic, 1>::Map(out, n));
        }

        static inline void project(MatrixSolver& OP, int n, int k, Scalar* vecs)
        {
            // Solve L^T out = in
            //
            Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.matrixU().solve(Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k));
            Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k) = OP.permutationPinv() * Matrix<Scalar, Dynamic, Dynamic>::Map(vecs, n, k);
        }
    };

    template <typename MatrixSolver, typename MatrixType, typename Scalar> struct OP<MatrixSolver, MatrixType, Scalar, false>
    {
        static inline void applyOP(MatrixSolver& OP, const MatrixType& A, int n, Scalar* in, Scalar* out)
        {
            eigen_assert(false && "Should never be in here...");
        }

        static inline void project(MatrixSolver& OP, int n, int k, Scalar* vecs) { eigen_assert(false && "Should never be in here..."); }
    };

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_ARPACKSELFADJOINTEIGENSOLVER_H
